cg6_2013 - Computer Graphics Lecture 6 View Transformation...

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Computer Graphics Lecture ± View Transformation and Clipping Taku Komura
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&verview • View transformation – Recap of homogeneous transformation – -arallel projection – -erspective projection – ±anonical view volume • ±lipping – 'ine / -olygon clipping
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Procedure ±² Transform into camera coordinates² ³done in Lecture ´µ ¶² Perform projection into Y`\Z YROXP\ or VzU\\Q zRRU[`QxW\V± ´² Clip geometry outside the Y`\Z YROXP\ ²
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View Projection ± Topics ●Homogenous transformation ●Parallel projection ●Perspective projection ●Canonical view volume
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±omogeneous Transformations Y.D SURa D Z≖z D z≖O Y O The projection matiix should be ±x± matrices to allow general concatenation
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±omogeneous ²oordinates
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Camera Coordinate System we use ±same as OpenGL² y z x Facing the –z direction X axis facing the right side
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Parallel projections ±Orthographic projection² • Specified by a direction of projection³ rather than a point´ • Objects of same size appear at the same size after the projection
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Parallel projection± Orthographic Projection onto a plane at z = ²± x p = x ³ y p = y ³ z = ²±
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Perspective Projection • Objects far away appear smaller± closer objects appear bigger • Specified by a center of projection and the focal distance ²distance from the eye to the projection plane³
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Perspective projection d y z Projectio n Plane± P²x³y³ P p ²x p ³y p ³µ Centre of projection at the origin³ Projection plane at z=µd± d¶ focal distance x
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Alternative formulation± z P²x³y³ d x x p z P²x³y³ d y y p Projection plane at z = µ³ Centre of projection at z = d Now we can allow d→∞
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Exercise± where will the two points be projected onto?
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Problems • After projection± the depth information is lost • We need to preserve the depth information for hidden surface removal • Objects behind the camera are projected to the front of the camera
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3± View Volume • The volume in which the visible objects exist – ²or parallel projection, view volume is a box.
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cg6_2013 - Computer Graphics Lecture 6 View Transformation...

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